Impacts of Covid-19 mode shift on road traffic

Yue Hu∗, Will Barbour∗, Samitha Samaranayake†, Dan Work∗

May 4, 2020

Abstract

This article is driven by the following question: as the communities reopen after the COVID-19pandemic, will changing transportation mode share lead to worse traffic than before? This questioncould be critical especially if many people rush to single occupancy vehicles. To this end, we estimatehow congestion will increases as the number of cars increase on the road, and identify the most sensitivecites to drop in transit usage. Travel time and mode share data from the American Community Surveyof the US Census Bureau, for metro areas across the US. A BPR model is used to relate average traveltimes to the estimated number of commuters traveling by car. We then evaluate increased vehicle volumeson the road if different portions of transit and car pool users switch to single-occupancy vehicles, andreport the resulting travel time from the BPR model. The scenarios predict that cities with large transitridership are at risk for extreme traffic unless transit systems can resume safe, high throughput operationsquickly.

1 Introduction

Traffic jams result when there are more vehicles than the road network can handle. After the roadsare fully saturated, the travel times increase with each additional traveler. In fact, the rate at whichtraffic grows follows a very predictable pattern. Similarly, when there is a steep decrease in the numberof travelers, traffic can vanish. The travel restrictions put in place to reduce the spread of Covid-19resulted in a sharp reduction in traffic throughout the US.

As communities begin to reopen, it is important to understand how badly traffic will rebound. Usingbasic laws of traffic, we can predict the amount of traffic that will occur in each city given only thenumber of vehicles on the road. This allows us to explore “what if” scenarios. For example, it is possiblethat many transit riders could switch to a car instead. We want to know how these decisions will impacttraffic.

To answer the above questions, we need to estimate the change in traffic volume caused by the dropof transit usage, and how this change will affect commute time on the road. With historical data of thenumber of commuters using each travel mode – carpool, transit or single-occupancy vehicle (SOV) – weare able to estimate the number of cars on the road if certain proportions of commuters switch fromtransit and carpool modes to SOV, thereby increasing the total number of vehicles. We assume that thenumber of commuting vehicles from these modes is representative of total traffic volume. This data isfit to the BPR model [1, 2] to capture the relationship between traffic volume and average travel time,allowing us to predict travel time under scenarios where the number of vehicles on the road decreases.

Several studies try to model the congested travel in urban network. Saberi et al. [3] use a susceptible-infected-recovered (SIR) model to describe the spreading of traffic jam. Colak et al. [4] use the ratioof road supply to travel demand as a dimensionless factor to explain the percentage of time lost incongestion. The macroscopic BPR model is studied by Wong et al. [5] and Kucharsk and Drabicki [6]to relate traffic demand and travel time. One or several cities or regions are studied in the above works,while our work compares the traffic congestion behavior for more than one hundred cities in US, andmake predictions for their travel time under various scenarios of possible traffic volume.

Our main finding is that high-transit cities are at greater risk for increased traffic unless their transitsystems can resume safe, high throughput operations quickly. Figure 1 gives a more detailed look at the

∗Vanderbilt University and Institute for Software Integrated Systems, Nashville, TN 37212†Cornell University, Ithaca, NY 14853

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Figure 1: Transit heavy congested cities are most at risk of travel time spikes. Travel times are given asone-way commute times. We assume two scenarios, where 1 in 4 and 3 in 4 commuters of transit and carpoolswitch to SOV, respectively.

consequences of the shift away from transit for these high-transit cities. The cities most at risk includeSan Francisco, New York, Los Angeles, Boston, Chicago, Seattle, and San Jose, with potentially 6-80minutes additional commute travel time per person on a one-way trip. We note that these potentialincreases are avoidable. If transit ridership returns in step with trips by car, road traffic will return tonormal. Monitoring closely road and transit ridership during the rebound is critical.

We also demonstrate our method and main findings in a more digestible format in article “TheRebound: How Covid-19 could lead to worse traffic”1 [7], where interactive plots are included to betterinterpret the results.

In the remainder of this article, we will introduce the formulation of BPR model (Section 2), introducethe data on traffic in US cities (Section 3.1) , and show the forecast result of traffic in different reopeningscenarios (Section 3.2).

2 Method: BPR model

The Bureau of Public Road (BPR) function [1, 2] is a model that relates the volume of traffic on theroad to the travel time to traverse it. It is widely used in transportation management [8, 9], and networktraffic simulation [10]. While the BPR model is mostly applied on single-road traffic, recent studies haveshown its applicability on urban scale transportation analysis [5, 6]. Thus, BPR function provides uswith theoretical foundation of predicting metro area travel congestion based on traffic volume.

The classic BPR function reads

τ = τf

(1 + α

(N

C

)β), (1)

1https://medium.com/@barbourww/the-rebound-how-covid-19-could-lead-to-worse-traffic-cb245a5b1da2

2

with τ the travel time as a function of N the volume on the roadway. The parameters τf , C are the freeflow travel time and the road capacity respectively. The shape parameters α and β can be fit or assumedto follow a common choice of α = 0.15 and β = 4.0 [1, 2].

For application at the scale of a city, we interpret the BPR model as a function that takes the totalnumber of road users in a city N as a proxy for volume, and returns the average commute travel time τin the city. In this interpretation, the capacity C should be viewed as the total number of road users thatcan be accommodated in the city before average travel times begin to increase. Note that the averagetravel time is over all users at all times of the day.

Next we show that the model parameters of the BPR function can be estimated using linear regression.Rewriting(1), we have

τ = τf

(1 +

0.15

C4

(N4)) , (2)

or with simplificationτ = τf + γ

(N4) . (3)

The form (3) shows that travel time τ and the fourth order of traffic volume N4 have a linearrelationship. With historic data of travel time and the number of road users, we can conduct linearregression to find the coefficients τf and γ. This in turn allows us to estimate the free flow travel time

τf and road capacity C =(

0.15τfγ

) 14

for each city, deducing from (2).

3 Experiment

3.1 Data description

All our data comes from American Community Survey (ACS) of the United States Census Bureau(USCB) [11], automatically downloaded via Julien Leider’s “censusdata” Python package [12]. The datarecords means of transportation to work by selected characteristics. For each metropolitan statisticalareas (MSA) [13], annually statistics of up to eight years (2010 - 2018) is recorded, including total numberof people for each commute mode (2-person carpool, 3-person carpool, single-occupancy vehicle (SOV),public transit, walk, and taxi/motorcycle/bike/other), as well as the average commute time for eachmode. We select metros areas with at least 4 years of records, resulting in 131 areas in total.

Using the raw data, we calculated the road commute metrics. For each metro area each year, themean travel time on the road is computed as a weighted average of carpool and SOV travel time. Totalnumber of vehicles is computed by converting 2-person carpool, 3-person carpool and SOV into equivalentvehicles on the road. We also estimated the resulting cars on the road when 25%, 50% and 75% of thecarpool and transit commuters switch to SOV. We note that we are using the statistics from 2018 toestimate the number of vehicles, which is the latest data available. We do not account in this analysis forgrowth from 2018 to present day, which can be considered in an extension. We also note that the modeshare data for taxis and ride hailing is mixed in with motorcycles, bike and others, but this categoryconstitutes only a small portion of the traffic volume (2% on average), so we omit the influence of taxisin this study, and do not count taxis in total number of vehicles.

Commute time for all metro areas in the US in 2018 are shown in Figure 2. We see that cities with alarge number of vehicles tend to have higher travel times. But the trends are not obvious, since the traveltime in each city depends on a number of factors, such as the size of the city, the population density, theaverage distance traveled, etc.

3.2 Model fitting and results

3.2.1 BPR model

To better understand the travel times, we now look at the behavior of individual cities. We show thatfor many cities, travel times follow the BPR model as described in Equation (2).

Firstly, we filter out metro areas that do no have strong relationship between traffic volume and traveltime over the years. There can be two two reasons for having no strong relationship. Firstly there mightbe error in data collection. Secondly the traffic network might not be saturated yet, so traffic volume isnot the main factor for increase in travel time. In these cases, traffic volume do no have predictive power

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Figure 2: Travel time vs. traffic volume for all metro areas in the US in 2018. Across cities, average traveltimes increase with more vehicles on the road.

for commute time prediction, so we chose to filter them out. The filtering is done as following. For eachmetro area, we measure the linear correlation between travel time τ and the fourth order of traffic volumeN4, and calculate their Pearson’s correlation coefficient and two-tailed p-value. We filter out the metroareas where Pearson’s correlation coefficient is larger than 0.5 and p-value is smaller than 0.1. Usingthis threshhold, 76 metro areas are selected, and 55 metro areas are not included for further analysis.We then fit the BPR model for the 76 selected metros. Figure 3 shows the result of four example metroareas. We can see how travel time grows with number of vehicles, nicely following the BPR function. Acomplete plot for BPR fit of each metro areas, as well as the estimated free flow travel time and roadcapacity can be found in appendix(Figure 8, 9, 10).

Using the estimated free flow travel time and road capacity, we calculate two important metrics foreach metro area:

• Travel time ratio: the ratio of actual travel time versus free flow travel time. A travel time ratio of1.1 means the current travel time is 1.1 times (or 10% higher) than the empty road travel time.

• Capacity ratio: the ratio of traffic volume versus road capacity. A capacity ratio of 1.1 means thereare 10% more cars than the road capacity.

Travel time ratio and capacity ratio allows us to standardize each city, accounting for the fact that largercities tend to have larger capacities and longer commutes, even when the roads are empty. Figure 4 showsthe standardized relationship of travel time ratio and capacity ratio across all metro areas. We see thatall of the cities now follow the same growing curve. Essentially, what we are doing in the standardization,is looking at the rate travel time ratio increases with capacity ratio, then estimate where the city sits onthe BPR curve. For example, for San Francisco there is a sharp increase in travel time ratio as capacityratio increases. This indicates that the traffic volume of San Francisco is way above road capacity. As aconsequence, in the standardized figure 4, San Francisco is the most upper right point.

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Figure 3: Four examples of BPR fitting for individual metro areas. The blue points are the observed data,and dashed line is the estimated BPR curve. We can see how travel time grows with number of vehicles,nicely following the BPR function.

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Figure 4: Travel time ratio vs. capacity ratio. This captures how road congestion level increases with trafficvolume. When number of cars do not excess road capacity, the travel time do not deviate too much freeflow. But once the number of cars is larger than road capacity, travel time begins to increase sharply. Themost upper right point is San Francisco, indicating that traffic volume is way above road capacity for SanFrancisco.

3.3 Traffic scenarios prediction during the rebound

We now explore what could happen if commuters quickly return to the roads, and transit users switchto SOV instead. We consider four scenarios, namely when 25%, 50%, 75% and 100% of the carpool andtransit commuters switch to SOV. We note that the scenarios are created to show a range of possibilities,not necessarily to predict the actual mode shift. The actual rate at which transit and carpool commutersshift to personal vehicles will depend on a multitude of factors that are specific to each traveler and eachcity, such as unemployment [14] and remote work [15]. In other words, we are not claiming that 75% or100% transit users will switch to SOV commutes. Rather, the intention is to identify which cities are themost sensitive to changes in the number of cars on the road.

The predictions for four example cities under each of the four scenarios is shown in Figure 5. Twomain factors determine if travel times will significantly increase:

• Cities that historically have high capacity ratios (many more cars than the network can handle)are naturally sensitive to changes in the number of cars on the road. Even small changes can havebig impacts. A typical example is Seattle as shown in Figure 5c

• Cities that historically have lower capacity ratios can also see travel time impacts if the number ofcars on the road increases enough. A large change will cause the travel times to increase substantiallyas well. A typical example is New York as shown in Figure 5b.

The bar plot in Figure 6 summarizes the travel time increase predictions for metros with medium/largetransit (public transit taking up more than 5% of total commuter). Generally, we see that the increasesare more severe for larger cities, and those that are more dependent on transit – 8 of 10 cities withthe largest predicted travel time increase also rank in the top 10 for transit use. The most extremescenario (when all riders switch) is extremely unlikely. But it does illustrate that keeping transit open,safe, and available will be important to control the traffic rebound. In the less extreme scenarios, we

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Figure 5: Four examples of BPR travel time prediction for individual metro areas. The blue points are theobserved data, and the red points are the predictions when 25%, 50%, 75% and 100% of the carpool andtransit commuters switch to SOV. Dashed line is the estimated BPR curve.

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Figure 6: Travel time increase predictions for metros with medium/large transit (public transit taking upmore than 5% of total commuter).

see that average travel times can increase by a few minutes. This might not seem like much, but it is.The additional delay is for each trip. When multiplied by the number of travelers in these cities, evena minute of delay per traveler can easily result in thousands of hours of additional time spent in trafficevery day.

4 Conclusions

In this work, we gather historical data from the the US Census Bureau, which includes data on thecommute mode and road travel times for cities in the US. A BPR model is used to relate average traveltimes to the estimated number of commuters traveling by car. We then estimate the number of carson the road if different portions of transit and car pool users switch to single-occupancy vehicles, andpredict the resulting travel time from the BPR model.

To conclude, our take-away messages are:• When the roads are already saturated above road capacity, increasing cars on the road is detrimental

to everyone’s commute. This is captured by the BPR model.• Covid-19 cleared the streets in many communities. As we reopen, traffic will eventually rebound.

If transit ridership does not return, travel times will increase, sometimes dramatically.• Travel time increases of 5-10 minutes are possible in high-transit cities, which adds up to hundreds

of thousands of hours of additional travel time each day• These increases are avoidable, if transit ridership resumes in step with car traffic.

Acknowledgements

This material is based upon work supported by the National Science Foundation under Grant No.CMMI-1727785.

References

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[2] Mark S Daskin. Urban transportation networks: Equilibrium analysis with mathematical program-ming methods. JSTOR, 1985.

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[4] Serdar Colak, Antonio Lima, and Marta C Gonzalez. Understanding congested travel in urbanareas. Nature communications, 7(1):1–8, 2016.

[5] Wai Wong and SC Wong. Network topological effects on the macroscopic bureau of public roadsfunction. Transportmetrica A: Transport Science, 12(3):272–296, 2016.

[6] Rafa l Kucharski and Arkadiusz Drabicki. Estimating macroscopic volume delay functions with thetraffic density derived from measured speeds and flows. Journal of Advanced Transportation, 2017,2017.

[7] The rebound: How covid-19 could lead to worse traffic. https://medium.com/@barbourww/

the-rebound-how-covid-19-could-lead-to-worse-traffic-cb245a5b1da2, 2020. Accessed:2020-4.

[8] Highway Capacity Manual. Highway capacity manual. Washington, DC, 2, 2000.

[9] Richard G Dowling, Rupinder Singh, and Willis Wei-Kuo Cheng. Accuracy and performance ofimproved speed-flow curves. Transportation research record, 1646(1):9–17, 1998.

[10] Michael Florian and Sang Nguyen. Recent experience with equilibrium methods for the study of acongested urban area. In Traffic Equilibrium Methods, pages 382–395. Springer, 1976.

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S0804, 2020. Accessed: 2020-4.

[12] Julien Leider. Censusdata python package. https://github.com/jtleider/censusdata, 2020. Ac-cessed: 2020-4.

[13] United States Census Bureau. About metropolitan and micropolitan. https://www.census.gov/

programs-surveys/metro-micro/about.html, 2020. Accessed: 2020-4.

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gov/ui/data.pdf, 2020. Accessed: 2020-4.

[15] Erik Brynjolfsson, J Horton, Adam Ozimek, Daniel Rock, Garima Sharma, and Hong Yi Tu Ye.Covid-19 and remote work: An early look at us data, 2020.

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Appendix

In this appendix, we attach the complete results for all cities. It includes plots of Travel time ratio vs.capacity ratio (Figure 7), BPR fit for each metro areas(Figure 8, Figure 9, and Figure 10), and bar plotof BPR predictions for all metro (Figure 11).

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Baltimore-Columbia-Towson, MD Metro AreaBoston-Cambridge-Newton, MA-NH Metro AreaDallas-Fort Worth-Arlington, TX Metro AreaTulsa, OK Metro AreaAustin-Round Rock, TX Metro AreaNorth Port-Sarasota-Bradenton, FL Metro AreaBoise City, ID Metro AreaOklahoma City, OK Metro AreaSeattle-Tacoma-Bellevue, WA Metro AreaMiami-Fort Lauderdale-West Palm Beach, FL Metro AreaSanta Rosa, CA Metro AreaAtlanta-Sandy Springs-Roswell, GA Metro AreaDetroit-Warren-Dearborn, MI Metro AreaMinneapolis-St. Paul-Bloomington, MN-WI Metro AreaOrlando-Kissimmee-Sanford, FL Metro AreaRaleigh, NC Metro AreaLincoln, NE Metro AreaVallejo-Fairfield, CA Metro AreaMemphis, TN-MS-AR Metro AreaLexington-Fayette, KY Metro AreaNashville-Davidson--Murfreesboro--Franklin, TN Metro AreaReading, PA Metro AreaAllentown-Bethlehem-Easton, PA-NJ Metro AreaBaton Rouge, LA Metro AreaFresno, CA Metro AreaHartford-West Hartford-East Hartford, CT Metro Area

Houston-The Woodlands-Sugar Land, TX Metro AreaSalinas, CA Metro AreaOgden-Clearfield, UT Metro AreaWorcester, MA-CT Metro AreaPortland-Vancouver-Hillsboro, OR-WA Metro AreaKansas City, MO-KS Metro AreaRichmond, VA Metro AreaSpokane-Spokane Valley, WA Metro AreaDurham-Chapel Hill, NC Metro AreaLas Vegas-Henderson-Paradise, NV Metro AreaDenver-Aurora-Lakewood, CO Metro AreaGreenville-Anderson-Mauldin, SC Metro AreaPhoenix-Mesa-Scottsdale, AZ Metro AreaTucson, AZ Metro AreaProvo-Orem, UT Metro AreaLancaster, PA Metro AreaSan Diego-Carlsbad, CA Metro AreaWashington-Arlington-Alexandria, DC-VA-MD-WV Metro AreaCharleston-North Charleston, SC Metro AreaSt. Louis, MO-IL Metro AreaColorado Springs, CO Metro AreaSalt Lake City, UT Metro AreaLos Angeles-Long Beach-Anaheim, CA Metro AreaOxnard-Thousand Oaks-Ventura, CA Metro AreaSan Francisco-Oakland-Hayward, CA Metro Area

Duluth, MN-WI Metro AreaSan Antonio-New Braunfels, TX Metro AreaJacksonville, FL Metro AreaRiverside-San Bernardino-Ontario, CA Metro AreaLouisville/Jefferson County, KY-IN Metro AreaOmaha-Council Bluffs, NE-IA Metro AreaAnn Arbor, MI Metro AreaBridgeport-Stamford-Norwalk, CT Metro AreaBoulder, CO Metro AreaSacramento--Roseville--Arden-Arcade, CA Metro AreaChicago-Naperville-Elgin, IL-IN-WI Metro AreaCincinnati, OH-KY-IN Metro AreaVirginia Beach-Norfolk-Newport News, VA-NC Metro AreaProvidence-Warwick, RI-MA Metro AreaRochester, MN Metro AreaSan Jose-Sunnyvale-Santa Clara, CA Metro AreaStockton-Lodi, CA Metro AreaBuffalo-Cheektowaga-Niagara Falls, NY Metro AreaPittsburgh, PA Metro AreaPhiladelphia-Camden-Wilmington, PA-NJ-DE-MD Metro AreaBremerton-Silverdale, WA Metro AreaCharlotte-Concord-Gastonia, NC-SC Metro AreaNew York-Newark-Jersey City, NY-NJ-PA Metro AreaSavannah, GA Metro AreaTampa-St. Petersburg-Clearwater, FL Metro Area

Figure 7: Travel time ratio vs. capacity ratio.

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Figure 8: BPR fit for each metro areas, part 1. The estimated free flow travel time and road capacity is alsoshown for each metro. The blue points are the observed data, and the grey points are the predictions when25%, 50% and 75% of the carpool and transit commuters switch to SOV. Red line is the estimated BPRcurve.

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Figure 9: BPR fit for each metro areas, part 2. The estimated free flow travel time and road capacity is alsoshown for each metro. The blue points are the observed data, and the grey points are the predictions when25%, 50% and 75% of the carpool and transit commuters switch to SOV. Red line is the estimated BPRcurve.

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Figure 10: BPR fit for each metro areas, part 3. The estimated free flow travel time and road capacity isalso shown for each metro. The blue points are the observed data, and the grey points are the predictionswhen 25%, 50% and 75% of the carpool and transit commuters switch to SOV. Red line is the estimatedBPR curve.

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0 20 40 60 80 100travel time (min)

San Francisco-Oakland-Hayward, CA Metro AreaNew York-Newark-Jersey City, NY-NJ-PA Metro Area

Boston-Cambridge-Newton, MA-NH Metro AreaSeattle-Tacoma-Bellevue, WA Metro Area

San Jose-Sunnyvale-Santa Clara, CA Metro AreaLos Angeles-Long Beach-Anaheim, CA Metro Area

Philadelphia-Camden-Wilmington, PA-NJ-DE-MD Metro AreaChicago-Naperville-Elgin, IL-IN-WI Metro Area

Atlanta-Sandy Springs-Roswell, GA Metro AreaBaltimore-Columbia-Towson, MD Metro Area

Miami-Fort Lauderdale-West Palm Beach, FL Metro AreaPortland-Vancouver-Hillsboro, OR-WA Metro Area

Houston-The Woodlands-Sugar Land, TX Metro AreaOrlando-Kissimmee-Sanford, FL Metro Area

Boulder, CO Metro AreaStockton-Lodi, CA Metro AreaBaton Rouge, LA Metro Area

Ann Arbor, MI Metro AreaNashville-Davidson--Murfreesboro--Franklin, TN Metro Area

Dallas-Fort Worth-Arlington, TX Metro AreaBremerton-Silverdale, WA Metro Area

San Diego-Carlsbad, CA Metro AreaAustin-Round Rock, TX Metro Area

Riverside-San Bernardino-Ontario, CA Metro AreaDenver-Aurora-Lakewood, CO Metro Area

Charleston-North Charleston, SC Metro AreaTampa-St. Petersburg-Clearwater, FL Metro Area

Pittsburgh, PA Metro AreaJacksonville, FL Metro Area

Oxnard-Thousand Oaks-Ventura, CA Metro AreaDurham-Chapel Hill, NC Metro Area

Savannah, GA Metro AreaSacramento--Roseville--Arden-Arcade, CA Metro Area

Vallejo-Fairfield, CA Metro AreaRaleigh, NC Metro Area

Detroit-Warren-Dearborn, MI Metro AreaSt. Louis, MO-IL Metro Area

North Port-Sarasota-Bradenton, FL Metro AreaSan Antonio-New Braunfels, TX Metro Area

Charlotte-Concord-Gastonia, NC-SC Metro AreaTucson, AZ Metro Area

Phoenix-Mesa-Scottsdale, AZ Metro AreaHartford-West Hartford-East Hartford, CT Metro Area

Richmond, VA Metro AreaVirginia Beach-Norfolk-Newport News, VA-NC Metro Area

Cincinnati, OH-KY-IN Metro AreaAllentown-Bethlehem-Easton, PA-NJ Metro Area

Minneapolis-St. Paul-Bloomington, MN-WI Metro AreaProvidence-Warwick, RI-MA Metro Area

Santa Rosa, CA Metro AreaLouisville/Jefferson County, KY-IN Metro Area

Reading, PA Metro AreaLancaster, PA Metro Area

Salt Lake City, UT Metro AreaLas Vegas-Henderson-Paradise, NV Metro Area

Memphis, TN-MS-AR Metro AreaOklahoma City, OK Metro Area

Kansas City, MO-KS Metro AreaBuffalo-Cheektowaga-Niagara Falls, NY Metro Area

Boise City, ID Metro AreaLincoln, NE Metro Area

Omaha-Council Bluffs, NE-IA Metro AreaProvo-Orem, UT Metro Area

Ogden-Clearfield, UT Metro Area

187.00%77.50%

49.82%45.63%

33.49%20.32%31.70%23.57%

9.88%16.23%

13.81%24.12%10.30%9.94%

18.57%10.20%6.67%10.16%4.77%7.46%21.35%11.66%8.34%9.56%8.51%4.63%8.13%10.07%9.62%18.41%7.07%9.22%6.89%10.42%7.31%2.81%7.57%10.93%7.81%1.47%9.52%4.91%7.73%5.69%5.47%6.09%10.02%3.41%12.86%12.54%5.84%12.93%14.65%5.56%4.97%1.66%

5.28%3.40%

7.21%5.41%

5.80%3.16%5.66%

1.30%

BPR model estimated time for all cities100%75%50%25%current time

Figure 11: BPR predictions for all metro areas when 25%, 50%, 75% and 100% of the carpool and transitcommuters switch to SOV.

14